Finite Group DatabasebetaFinite Group Databasebeta| order | 3328 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C13 · Schur multiplier (H2) = C28 |
| direct product | C13×#61665 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C13 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C13 |
| prime radical | C13×#3499 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C13×#532 ◁ G | |
2008 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1664 |
A minimal faithful permutation representation — 5 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,20)(17,19)(18,21)(22,23,28,32)(24,29,35,45)(25,36,38,46)(26,31,27,40)(30,41,47,37)(33,48,51,53)(34,43,39,44)(42,49,52,50);(14,16)(15,18)(17,21)(19,20)(22,24)(23,29)(25,33)(26,39)(27,34)(28,35)(30,42)(31,44)(32,45)(36,48)(37,50)(38,51)(40,43)(41,49)(46,53)(47,52);(22,25,28,38)(23,30,32,47)(24,33,35,51)(26,37,27,41)(29,42,45,52)(31,46,40,36)(34,49,39,50)(43,48,44,53);(16,21)(18,20)(22,24)(23,29)(25,33)(26,39)(27,34)(28,35)(30,42)(31,44)(32,45)(36,48)(37,50)(38,51)(40,43)(41,49)(46,53)(47,52);(15,19)(18,20)(22,26,28,27)(23,31,32,40)(24,34,35,39)(25,37,38,41)(29,43,45,44)(30,46,47,36)(33,49,51,50)(42,48,52,53)676 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3328, 54653);